Correlation-driven electronic states in "flat-band" quasicrystals

Flat-band systems provide a unique platform to investigate strongly-correlated quantum matter, since even weak electronic interactions can cause very strong effects. Quasicrystals offer an interesting window into this rich problem, since several of them display a macroscopic number of zero-energy states with non-trivial real-space structures, which play a role analogous to flat bands in regular crystals. In this work, we perform unbiased Quantum Monte Carlo (QMC) simulations of both the repulsive and attractive Hubbard models on different types of Penrose tilings with distinct zero-energy-states properties. By comparing the spin, charge and pairing ordering tendencies in each case, extracted from QMC correlation and spectral functions, we provide a comprehensive phase diagram of the superconducting and Mott insulating instabilities of quasicrystals, highlighting the important role played by the zero-energy states.